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SUMMARY:Kinetic Models of Dilute Polymers:  Analysis\, Approximation and C
 omputation - Endre Süli (Oxford)
DTSTART:20091119T150000Z
DTEND:20091119T160000Z
UID:TALK21069@talks.cam.ac.uk
CONTACT:6743
DESCRIPTION:We review recent analytical and computational results for\nmac
 roscopic-microscopic bead-spring models that arise from\nthe kinetic theor
 y of dilute solutions of incompressible\npolymeric fluids with noninteract
 ing polymer chains\, involving\nthe coupling of the unsteady Navier–Stok
 es system in a\nbounded $d$-dimensional domain $\\Omega$\,\n$d=2$ or 3\, w
 ith an elastic extra-stress tensor as\nright-hand side in the momentum equ
 ation\, and a\n(possibly degenerate) Fokker--Planck equation over the\n$(2
 d+1)$-dimensional region $\\Omega \\times D \\times [0\,T]$\,\nwhere $D \\
 subset \\mathbb{R}^d$ is the configuration domain\nand $[0\,T]$ is the tem
 poral domain. The Fokker--Planck\nequation arises from a system of (It$\\h
 at{\\rm o}$) stochastic\ndifferential equations\, which models the evoluti
 on of a\n$2d$-component vectorial stochastic process comprised by the\n$d$
 -component centre-of-mass vector and the $d$-component\norientation (or co
 nfiguration) vector of the polymer chain.\nWe show the existence of global
 -in-time weak solutions to\nthe coupled Navier--Stokes--Fokker--Planck sys
 tem for a\ngeneral class of spring potentials including\, in particular\,\
 nthe widely used finitely extensible nonlinear elastic\n(FENE) potential. 
 The numerical approximation of this\nhigh-dimensional coupled system is a 
 formidable computational\nchallenge\, complicated by the fact that for pra
 ctically\nrelevant spring potentials\, such as the FENE potential\, the\nd
 rift term in the Fokker--Planck equation is unbounded\non $\\partial D$. T
 he talk is based on joint work with\nJohn W. Barrett (Imperial College Lon
 don) and\nDavid J. Knezevic (Massachusetts Institute of Technology).\n
LOCATION:MR14\, CMS
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